Question

Select the correct answer.Which point satisfies the system of equations y= 3x - 2 and y=-2x + 3?98А7B6с5431D-9 8 7-65-4-3-2.111234 5 6 7 8 9Xr_ £ ܀ _\ ܀-6

Answer 1

At the point of intersection, the value of y for the systems of equations is the same. Hence, we can relate the two equations as

`\begin{gathered} y=3x-2,y=-2x+3 \\ 3x-2=-2x+3 \end{gathered}`

Solve for the value of x for the point of intersection, we have

`\begin{gathered} 3x+2x=3+2 \\ 5x=5 \\ x=1 \end{gathered}`

Use one of the equations on the systems of equations to solve for y. In this case, I will use y = 3x -2. Solve for y, we get

`\begin{gathered} y=3(1)-2 \\ y=1 \end{gathered}`

Hence, the point of intersection of the two equations is in (1,1) which is described by point D.